I'd suggest taking out the blower fan and do a visual inspection. Its not too hard to take it out, took me about 20 minutes. Hook it up and power it up with the new part and see if it spins fine or not. You'll find out pretty quick if the fan/motor is adding a burning smell.

I have a similar issue. Mine does the same thing and it only blows one direction which is everywhere. It blows defrost, floor, and dash at the same time along with only blowing on high. Any suggestions on this extra issue?